What is the resistance of a 20-mile aluminum wire transmission line?

[kriegera]

Homework Statement

A transmission line is made of aluminum wire 1 inch in diameter. What is the resistance of 20 miles of this wire?

Homework Equations

Resistance varies directly with the length of a wire and inversely with its cross-sectional area.
Resistivity of aluminum = 2.8 x 10-8
R=pl/A
Where l=32,186.88 meters
Find cross-sectional area.

R= 2.8 x 10-8 (31,186.88)/A =

The Attempt at a Solution

I'm stuck trying to find the cross-sectional area, A.

Also, the answer has to be in the same units as the problem, so does that mean I have to convert to inches and miles? The answer should be in ohms correct?

 

[rock.freak667]

The wire is like a long shaft or a long cylinder, so the cross-sectional area is?

Also, you need to convert everything to same set of units. What is the resistivity measured in?

 

[kriegera]

The wire is like a long shaft or a long cylinder, so the cross-sectional area is?

Also, you need to convert everything to same set of units. What is the resistivity measured in?

The cross-sectional area would be the diamter then? Converted to meters, we get


R= 2.8 x 10-8 (32,186.88)/0.0254 = .0354816 ohm-metres

correct?

 

[rock.freak667]

The cross-sectional area would be the diamter then?

No, the cross-section of the wire is just a circle with diameter 'd'. So the area of a circle is ?

 

[kriegera]

No, the cross-section of the wire is just a circle with diameter 'd'. So the area of a circle is ?

SO - Cross-Sectional Area= = Area: (pi)(.0127) ² = 5.067E-4

R= 2.8 x 10-8 (32,186.88)/ 5.067E-4 = 1.79 ohm-metres

 

[rock.freak667]

Yes that should be correct now.